An AMP-Based Asymptotic Analysis For Nonlinear One-Bit Precoding

2026-01-19

AI Summary

This work addresses the lack of precise asymptotic performance analysis for nonlinear 1-bit precoding over Rayleigh fading channels. By constructing a precoding model based on convex relaxation followed by quantization (CRQ), the study innovatively embeds the problem within an approximate message passing (AMP) framework. For the first time, the statistical behavior of the system in the large-system limit is reduced to a scalar “signal plus Gaussian noise” equivalent model. Leveraging this simplification, a closed-form expression for the symbol error probability is derived, enabling systematic quantification of how key parameters affect performance. Theoretical predictions are validated through simulations and shown to be highly accurate. Moreover, with appropriate parameter optimization, the proposed scheme outperforms the classical SQUID precoder.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Non-convex Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

This paper focuses on the asymptotic analysis of a class of nonlinear one-bit precoding schemes under Rayleigh fading channels. The considered scheme employs a convex-relaxation-then-quantization (CRQ) approach to the well-known minimum mean square error (MMSE) model, which includes the classical one-bit precoder SQUID as a special case. To analyze its asymptotic behavior, we develop a novel analytical framework based on approximate message passing (AMP). We show that, the statistical properties of the considered scheme can be asymptotically characterized by a scalar ``signal plus Gaussian noise''model. Based on this, we further derive a closed-form expression for the symbol error probability (SEP) in the large-system limit, which quantitatively characterizes the impact of both system and model parameters on SEP performance. Simulation results validate our analysis and also demonstrate that performance gains over SQUID can be achieved by appropriately tuning the parameters involved in the considered model.

Problem

• one-bit precoding
• asymptotic analysis
• symbol error probability
• Rayleigh fading
• nonlinear precoding

Innovation

• approximate message passing (AMP)
• one-bit precoding
• convex-relaxation-then-quantization (CRQ)
• asymptotic analysis
• symbol error probability (SEP)